Electric arc welding is used in a wide variety of metal jointing and surfacing applications. In most welding applications, the electrode is manipulated with respect to the welded joint, in order to achieve a desired weld bead profile. One form of electrode manipulation is weaving the electrode side to side across the weld joint serving to manipulate the heat of the arc and spread out the weld bead. In some of welding applications, this weaving motion is delayed at one or both edges of the weld. In practice, this delay is called a dwell. A weave technique is implemented in practice by many methods. Semi-automatically, the welder manipulates the torch back and forth across the weld joint while moving the torch along the weld joint. Many levels of mechanization are also commercially available. These machines mechanically weave the welding torch back and forth while also moving the electrode along the weld joint. Most welding robots offer several weave patterns as a standard feature. A weave technique is commonly used in a host of various joining and surfacing applications. The specific weave technique used as well as the specific effect obtained from the weave will depend on the application. Examples include open root butt joints where the electrode is weaved across the open joint and held on either side to achieve good penetration into the two workpieces to be joined without burning through the joint. When welding out-of-position fillet joints, the weave is used to focus the heat of the arc away from the center of the weld to obtain a relatively flat bead shape. In overlay and hardfacing applications, a weave is used to deposit weld metal across a large surface with minimal admixture from the base metal. In all of these examples, a weave technique was used to manipulate the heat of the arc away from the center of the weld joint and toward the edges of the weld. But the effect of using a weave technique is limited by how much of this heat can be manipulated by movement along. Thus there is a need for an improved welding system and method that further differentiates the heat input between the edges of a weave technique and the center.